We are not aware of a technique to solve this bound-constrained optimization problem directly.
Linear programming [1]} is a popular method to minimize an objective function with bounds, and also supports (in)equality constraints.
However, the objective function must consist of a single row, but we need to minimize independently per angle, and at once, so we have a matrix with multiple rows.
We therefore apply constrained least squares [2]}, [3]} to solve for the first two equations, and then augment that technique with bounds. By defining Lagrangian multipliers for the linear equation \(\mathbf {Cx-b=0}\)  and setting its derivatives to zero we can transform:
\(\min _\mathbf {x} \Vert \mathbf {Hx}-\mathbf {y}\Vert _2^2 \text{s.t.} \mathbf {Cx-b=0}\) 
